A sampling approach to biases in conditional probability judgments: Beyond base rate neglect and statistical format.

Abstract

Conditional probability judgments of rare events are often inflated when some meaningful relation exists between the condition and the low-baserate event. While traditional explanations assume that human judgments are generally insensitive to statistical baserates, more recent evidence shows much better performance when the problems are presented in natural frequency (as opposed to probability) formats and when the conditions refer to natural categories. The theory advanced here suggests a different explanation. Rather than postulating an a priori advantage of natural formats or categories, we emphasize sampling decisions as a key to understanding biased probability judgments. Experiment 1 shows that the seeming advantage of frequencies over probabilities is confined to conditions in which probabilities are scaled with reference to unequal subsamples. In Experiment 2, an active information search paradigm is employed that always provides a natural frequency format. When sampling by the predictor condition, the conditional probability to be estimated, p(criterion/ predictor), is conserved in the samples and the resulting judgments are quite accurate. However, when sampling by the criterion, the low-baserate event is strongly overrepresented in the samples. This sampling bias is even stronger than the resulting judgment bias. In general, judgments reflect the statistics of the actually acquired samples rather accurately, but judges do not understand the logical constraints imposed by their own sampling. This interpretation is corroborated in Experiment 3, where judges can freely choose between predictor sampling and criterion sampling, and in Experiment 4 using direct evaluations of the appropriateness of different sampling procedures.